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Analysis and Stochastics of Growth Processes and Interface Models$
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Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer

Print publication date: 2008

Print ISBN-13: 9780199239252

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199239252.001.0001

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Ballistic Phase of Self-Interacting Random Walks

Ballistic Phase of Self-Interacting Random Walks

Chapter:
(p.55) 3 Ballistic Phase of Self-Interacting Random Walks
Source:
Analysis and Stochastics of Growth Processes and Interface Models
Author(s):

Dmitry Ioffe

Yvan Velenik

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199239252.003.0003

The chapter presents a unified approach to a study of ballistic phase for a large family of self-interacting random walks with a drift and self-interacting polymers with an external stretching force. The approach is based on a recent version of the Ornstein–Zernike theory. It leads to local limit results for various observables (e.g. displacement of the end-point or number of hits of a fixed finite pattern) on paths of n-step walks (polymers) on all possible deviation scales from CLT to LD. The class of models, which display ballistic phase in the ‘universality class’ discussed in the chapter, includes self-avoiding walks, Domb–Joyce model, random walks in an annealed random potential, reinforced polymers, and weakly reinforced random walks.

Keywords:   ballistic phase, Ornstein–Zernike theory, self-avoiding walks, self-interacting polymers

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